Computation of the Unsteady Transonic Flow in Harmonically Oscillating Turbine Cascades Taking Into Account Viscous Effects

1996 ◽  
Author(s):  
B. Grüber ◽  
V. Carstens
Keyword(s):  
Transonic Flow ◽  
Splitting Method ◽  
Euler Method ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Implicit Time ◽  
Test Case ◽  
Turbine Cascade ◽  
Viscous Effects ◽  
Unsteady Pressure

This paper presents the numerical results of a code for computing the unsteady transonic viscous flow in a two-dimensional cascade of harmonically oscillating blades. The flow field is calculated by a Navier-Stokes code, the basic features of which are the use of an upwind flux vector splitting scheme for the convective terms (Advection Upstream Splitting Method), an implicit time integration and the implementation of a mixing length turbulence model. For the present investigations two experimentally investigated test cases have been selected in which the blades had performed tuned harmonic bending vibrations. The results obtained by the Navier-Stokes code are compared with experimental data, as well as with the results of an Euler method. The first test case, which is a steam turbine cascade with entirely subsonic flow at nominal operating conditions, is the fourth standard configuration of the “Workshop on Aeroelasticity in Turbomachines”. Here the application of an Euler method already leads to acceptable results for unsteady pressure and damping coefficients and hence this cascade is very appropriate for a first validation of any Navier-Stokes code. The second test case is a highly-loaded gas turbine cascade operating in transonic flow at design and off-design conditions. This case is characterized by a normal shock appearing on the rear part of the blades’s suction surface, and is very sensitive to small changes in flow conditions. When comparing experimental and Euler results, differences are observed in the steady and unsteady pressure coefficients. The computation of this test case with the Navier-Stokes method improves to some extent the agreement between the experiment and numerical simulation.

Computation of the Unsteady Transonic Flow in Harmonically Oscillating Turbine Cascades Taking Into Account Viscous Effects

1998 ◽  
Vol 120 (1) ◽  
pp. 104-111 ◽  
Author(s):  
B. Gru¨ber ◽  
V. Carstens
Keyword(s):  
Transonic Flow ◽  
Splitting Method ◽  
Euler Method ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Implicit Time ◽  
Test Case ◽  
Turbine Cascade ◽  
Viscous Effects ◽  
Unsteady Pressure

This paper presents the numerical results of a code for computing the unsteady transonic viscous flow in a two-dimensional cascade of harmonically oscillating blades. The flow field is calculated by a Navier–Stokes code, the basic features of which are the use of an upwind flux vector splitting scheme for the convective terms (Advection Upstream Splitting Method), an implicit time integration, and the implementation of a mixing length turbulence model. For the present investigations, two experimentally investigated test cases have been selected, in which the blades had performed tuned harmonic bending vibrations. The results obtained by the Navier–Stokes code are compared with experimental data, as well as with the results of an Euler method. The first test case, which is a steam turbine cascade with entirely subsonic flow at nominal operating conditions, is the fourth standard configuration of the “Workshop on Aeroelasticity in Turbomachines.” Here the application of an Euler method already leads to acceptable results for unsteady pressure and damping coefficients and hence this cascade is very appropriate for a first validation of any Navier–Stokes code. The second test case is a highly loaded gas turbine cascade operating in transonic flow at design and off-design conditions. This case is characterized by a normal shock appearing on the rear part of the blades’s suction surface, and is very sensitive to small changes in flow conditions. When comparing experimental and Euler results, differences are observed in the steady and unsteady pressure coefficients. The computation of this test case with the Navier–Stokes method improves to some extent the agreement between the experiment and numerical simulation.

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
A. Ghidoni ◽  
A. Colombo ◽  
S. Rebay ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
High Order ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

The Impact of Viscous Effects on the Aerodynamic Damping of Vibrating Transonic Compressor Blades—A Numerical Study

2000 ◽  
Vol 123 (2) ◽  
pp. 409-417 ◽  
Author(s):  
Bjo¨rn Gru¨ber ◽  
Volker Carstens
Keyword(s):  
Boundary Layer ◽  
Turbulence Model ◽  
Navier Stokes ◽  
Implicit Time ◽  
Compressor Cascade ◽  
Viscous Effects ◽  
Aerodynamic Forces ◽  
Aerodynamic Damping ◽  
Transonic Compressor ◽  
The Impact

A parametric study which investigates the influence of viscous effects on the damping behavior of vibrating compressor cascades is presented here. To demonstrate the dependence of unsteady aerodynamic forces on the flow viscosity, a computational study was performed for a transonic compressor cascade of which the blades underwent tuned pitching oscillations while the flow conditions extended from fully subsonic to highly transonic flow. Additionally, the reduced frequency and Reynolds number were varied. In order to check the linear behavior of the aerodynamic forces, all calculations were carried out for three different oscillation amplitudes. Comparisons with inviscid Euler results helped identify the influence of viscous effects. The computations were performed with a Navier-Stokes code, the basic features of which are the use of an AUSM upwind scheme, an implicit time integration, and the implementation of the Baldwin-Lomax turbulence model. In order to demonstrate the possibility of this code to correctly predict the unsteady behavior of strong shock-boundary layer interactions, the experiment of Yamamoto and Tanida on a self-induced shock oscillation due to shock-boundary layer interaction was calculated. A significant improvement in the prediction of the shock amplitude was achieved by a slight modification of the Baldwin Lomax turbulence model. An important result of the presented compressor cascade investigations is that viscous effects may cause a significant change in the aerodynamic damping. This behavior is demonstrated by two cases in which an Euler calculation predicts a damped oscillation whereas a Navier-Stokes computation leads to an excited vibration. It was found that the reason for these contrary results are shock-boundary-layer interactions which dramatically change the aerodynamic damping.

Aerodynamic Damping Predictions Using a Linearized Navier-Stokes Analysis

1999 ◽  
Author(s):  
Daniel Hoyniak ◽  
William S. Clark
Keyword(s):  
Experimental Data ◽  
High Speed ◽  
Operating Conditions ◽  
The Other ◽  
Navier Stokes ◽  
Turbine Cascade ◽  
Blade Loading ◽  
Operating Condition ◽  
Linear Cascade ◽  
Aerodynamic Damping

A recently developed two dimensional, linearized Navier-Stokes algorithm, capable of modeling the unsteady flows encountered in turbomachinery applications, has been benchmarked and validated for use in the prediction of the aerodynamic damping. Benchmarking was accomplished by comparing numerical simulations with experimental data for two geometries. The first geometry investigated is a high turning turbine cascade. For this configuration, two different steady operating conditions were considered. The exit flow for one operating condition is subsonic whereas the exit flow for the other operating condition is supersonic. The second geometry investigated is a tip section from a high speed fan. Again, two separate steady operating conditions were examined. For this fan geometry, one operating condition falls within an experimentally observed flutter region whereas the other operating condition was observed experimentally to be flutter free. For both geometries considered, experimental measurements of the unsteady blade surface pressures were acquired for a linear cascade subjected to small amplitude torsional vibrations. Comparisons between the numerical calculations and the experimental data demonstrate the ability of the present computational model to predict accurately the steady and unsteady blade loading, and hence the aerodynamic damping, for each configuration presented.

scholarly journals Simulations of Aeroelasticity in an Annular Cascade Using a Parallel 3-Dimensional Navier-Stokes Solver

2002 ◽  
Author(s):  
Ivan McBean ◽  
Feng Liu ◽  
Kerry Hourigan ◽  
Mark Thompson
Keyword(s):  
Unsteady Flow ◽  
Flow Model ◽  
Standard Test ◽  
Navier Stokes ◽  
Test Case ◽  
Turbine Cascade ◽  
3 Dimensional ◽  
Flow Through ◽  
The Stability ◽  
Annular Cascade

A parallel multi-block Navier-Stokes solver with the k-ω turbulence model is developed to simulate the 3-dimensional unsteady flow through an annular turbine cascade. Results at mid-span are compared with the experimental results of Standard Test Case 4. Comparisons are made between 3-dimensional and 2-dimensional, and inviscid and viscous simulations. The inclusion of a viscous flow model does not greatly affect the stability of the configuration.

Assessment of Laminar-Turbulent Transition Models for Turbomachinery Flow Computations

2005 ◽  
Author(s):  
L. Cutrone ◽  
P. De Palma ◽  
G. Pascazio ◽  
M. Napolitano
Keyword(s):  
Incompressible Flows ◽  
Navier Stokes ◽  
Test Case ◽  
Bypass Transition ◽  
Turbine Cascade ◽  
Turbulent Transition ◽  
Complex Test ◽  
Flow Through ◽  
Transition Models ◽  
Intermittency Factor

This paper provides a thorough comparison of different laminar-to-turbulent bypass transition models. The models are based on combinations of two transition-onset correlations and three intermittency factor models. They have been embedded in a Reynolds averaged Navier–Stokes solver employing a low-Reynolds number k–ω turbulence model. The performance of the transition models have been validated by computing three well documented incompressible flows over a flat plate, namely, test T3A, T3B, and T3C2 of ERCOFTAC SIG 10, with different free-stream conditions, the latter being characterized by non-zero pressure gradient. Finally, a more complex test case, namely the two-dimensional compressible flow through a linear turbine cascade, has been considered, for which detailed experimental data are available in the literature.

Implicit numerical simulation of transonic flow through turbine cascades on unstructured grids

2005 ◽  
Vol 219 (1) ◽  
pp. 35-47 ◽  
Author(s):  
Y Mei ◽  
A Guha
Keyword(s):  
Numerical Simulation ◽  
Finite Volume ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
Navier Stokes Equations ◽  
Flow Through

Numerical simulation of the compressible flow through a turbine cascade is studied in the present paper. The numerical solution is performed on self-adaptive unstructured meshes by an implicit method. Computational codes have been developed for solving Euler as well as Navier-Stokes equations with various turbulence modelling. The Euler and Navier-Stokes codes have been applied on a standard turbine cascade, and the computed results are compared with experimental results. A hybrid scheme is used for spatial discretization, where the inviscid fluxes are discretized using a finite volume method while the viscous fluxes are calculated by central differences. A MUSCL-type approach is used for achieving higher-order accuracy. The effects of the turbulent stress terms in the Reynolds-averaged Navier-Stokes equations have been studied with two different models: an algebraic turbulence model (Baldwin-Lomax model) and a two-equation turbulence model ( k-ɛ model). The system of linear equations is solved by a Gauss-Seidel algorithm at each step of time integration. A new treatment of the non-reflection boundary condition is applied in the present study to make it consistent with the finite volume flux calculation and the implicit time discretization.

Comparison of Theoretical and Experimental Data for an Oscillating Transonic Compressor Cascade

1999 ◽  
Author(s):  
Volker Carstens ◽  
Stefan Schmitt
Keyword(s):  
Experimental Data ◽  
Transonic Flow ◽  
Operating Conditions ◽  
Experimental Investigations ◽  
Test Case ◽  
Flow Conditions ◽  
Compressor Cascade ◽  
Blade Passage ◽  
Aerodynamic Damping ◽  
Transonic Compressor

Numerical and experimental results are compared for a compressor cascade performing harmonic oscillations in transonic flow. The flow field was calculated by a Q3D Navier Stokes code, the basic features of which are the use of an upwind flux difference scheme for the convective terms, the implementation of an effective one-equation turbulence model and the use of deforming multi-block grids. The experimental investigations were performed in an annular cascade windtunnel where unsteady blade pressures were measured for two different operating conditions of the cascade. The present data were all obtained for tuned torsional modes where the blades performed pitching oscillations with the same frequency and amplitude, but with a constant interblade phase angle. In the first test case the steady flow around the blades was purely subsonic. For the second test case the compressor cascade was run under transonic flow conditions where a normal shock in the front part of the blades’ suction side is followed by a blade passage shock. It becomes apparent that under subsonic flow conditions the predicted aerodynamic damping coefficients are in resonable agreement with the experimental data, although the numerical pressure amplitudes are much higher than the measured ones. In transonic flow significant discrepancies between computed and experimentally determined pressure amplitudes are observed, whereas the accuracy of the pressure phase prediction is comparable to the subsonic test case. Another important result of these investigations is that oscillations of the blade passage shock lead to strong variations of the local aerodynamic damping of the blades, but do not significantly change the global damping coefficient of the tested compressor cascade.

Investigation of Numerical and Physical Modelling Effects on the CFD Simulation of the Unsteady Flow in a HPT Stage

2003 ◽  
Author(s):  
P. de la Calzada ◽  
J. Ferna´ndez-Castan˜eda
Keyword(s):  
Unsteady Flow ◽  
Cfd Simulation ◽  
Stokes Equations ◽  
Physical Modelling ◽  
High Sensitivity ◽  
Potential Interaction ◽  
Navier Stokes ◽  
Test Case ◽  
Viscous Effects ◽  
Navier Stokes Equations

In order to investigate the unsteady flow behaviour in an HPT stage and the effects on the CFD solution of some numerical and physical modelling assumptions usually undertaken by the engineering community, an ITP in-house unsteady CFD code called Mu2s2T is first validated and then run under different configurations. The code is a fully unstructured code which solves the Reynolds averaged Navier-Stokes equations with a k-ω turbulence model. Hybrid meshes are used by having semi-structured meshes along the profile wall and fully unstructured triangular meshes on the inviscid region. The VKI Brite Euram transonic turbine stage experimental test case is used for the investigation. This turbine is representative of a state of the art HPT and presents high potential interaction due to the vane shock waves. After validating the code in this case, the influence of typical engineering assumptions is investigated. First the influence of the rotor stagger angle is analysed, resulting in a high sensitivity of the predicted pressure level at the front part of the blade and a better matching with the experimental data when an opening of 1° is applied. The influence in the solution of applying an integer airfoil count ratio compared with the solution with exact number off computed by means of phase lagged boundary conditions is also investigated. Additional Euler and Navier-Stokes computations are presented and the influence of the viscous effects is discussed. Finally a simulation including vane trailing edge cooling is performed so that conclusions about the influence of the cooling can be drawn.

Validation of a Navier-Stokes Solver for CFD Computations of Transonic Compressors

2006 ◽  
Author(s):  
Roberto Biollo ◽  
Ernesto Benini
Keyword(s):  
Numerical Model ◽  
Flow Field ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Operating Conditions ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Test Case ◽  
Complex Flow

The progress of numerical methods and computing facilities has led to using Computational Fluid Dynamics (CFD) as a current tool for designing components of gas turbine engines. It is known, however, that a sophisticated numerical model is required to well reproduce the many complex flow phenomena which characterize compression systems, such as shock waves and their interactions with boundary layers and tip clearance flows. In this work, the flow field inside the NASA Rotor 37, a well known test case representative of complex three-dimensional viscous flow structures in transonic bladings, was simulated using a commercial CFD code based on the 3-D Reynolds-averaged Navier-Stokes equations. In order to improve the accuracy of predictions, different aspects of the numerical model were analyzed; in particular, an attempt was made to understand the influence of grid topology, number of nodes and their distribution, turbulence model, and discretization scheme of numerical solution on the accuracy of computed results. Existing experimental data were used to assess the quality of the solutions. The obtainment of a good agreement between computed and measured performance maps and downstream profiles was clearly shown. Also, detailed comparisons with experimental results indicated that the overall features of the three-dimensional shock structure, the shock-boundary layer interaction, and the wake development can be calculated very well in the numerical approach for all the operating conditions. The possibility for a numerical model to better understand the aerodynamic behaviour of existing transonic compressors and to help the design of new configurations was demonstrated. It was also pointed out that the development of an accurate model requires the knowledge of both the physical phenomena place within the flow field and the features of the code which model them.

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